But can the Senate do that? There's reason to think not, and here's why.

In January 1967, Adam Clayton Powell of New York was re-elected by the Harlem district he represented since 1942, despite allegations that he had misused official travel funds and made improper payments to his wife. The House, invoking a provision of the Constitution that says, "Each House shall be the Judge of the Elections, Returns and Qualifications of its own Members," decided that Powell was unqualified and refused to seat him, declaring the seat vacant.

So, he sued.

The Supreme Court ruled -- by a vote of 8 to 1 -- that the House was wrong and that Powell must be seated. The court said in deciding whether to exclude, Congress is limited to considering only whether a member meets the very minimal requirements for office set out in the Constitution.

There have been other cases in which Congress refused to seat incoming members based on allegations of irregularities in elections, and many legal experts believe Congress has the Constitutional authority to examine potential election violations.

But given that Blagojevich is still legally the governor of Illinois and has the sole power to fill vacancies in the U.S. Senate, the Senate's power to refuse to seat his appointee may be far more limited than the leadership was implying.